
Organisers
D.C. Brydges (UBC)
J. Feldman (UBC)
A. van Enter
(Groningen)
Dates: July 6  10,
2009
Principal
Topics: Equilibrium
statistical mechanics, the renormalisation group,
properties and existence, hierarchical models in probability
Objectives
In
equilibrium statistical mechanics models are classified into classes
by their scaling limits of their critical points. These classes are
called Universality Classes
and a major problem in equilibrium statistical mechanics is to
characterise these classes. Much of theoretical physics is built around
the renormalisation group (RG). In physics, it is a heuristic, but
systematic,
scheme for calculating properties of scaling limits, in particular
critical exponents. In mathematics, it is a basic tool for proving
existence of scaling limits. From a probabilistic view scaling
limits are
important because they are generalisations of the Gaussian
distribution and its role in the central limit theorem.
The RG leads
naturally to the study of models on lattices with
ultrametrics, also called hierarchical models, which are of independent
interest as probabilistic models of evolution.
Mathematical attempts
at justifying the physics heuristics have in
various cases run into trouble, due to unexpected (non)existence
problems, having to do with nonlocalities. Such
"nogo" results
often show up by the occurrence of nonGibbsian states, which have
become a topic of independent interest.
The topics for
this workshop include
Gibbsian properties of renormalised and scaling limit distributions, hierarchical models,
universality classes for two dimensional models, random
Schroedinger operators, correlations for crystals at finite
temperature, Bose Einstein condensation.
